Z 分数计算

Question

How to calculate the Z-Score of a particular Column(x Variable). The formula is (x-mu)/sigma. What should be the value of the x here? My X variable column contains 24 values(rows). Should i take all the Summation of X values and then use it in the above formula? Pleas let me know.

Thanks

Answer 1

Z score is basically centering the values around the mean and scaled by standard deviation. You will find the mean, sd of your variable and convert all of your values to a z-score, for example:

import pandas as pd
import numpy as np
df = pd.DataFrame({'x':np.random.uniform(0,1,100)})
df['z_score_1'] = (df['x'] - df['x'].mean())/df['x'].std(ddof=1)

You can also use scipy, note I set degree of freedom to be 1 in both cases to use the unbiased estimator of standard deviation:

from scipy.stats import zscore
df['z_score_2'] = zscore(df['x'],ddof=1)

df[:5]

    x           z_score_1   z_score_2
0   0.543405    0.244382    0.244382
1   0.278369    -0.667379   -0.667379
2   0.424518    -0.164608   -0.164608
3   0.844776    1.281142    1.281142
4   0.004719    -1.608777   -1.608777